A hybrid vehicle is known that has a clutch disposed between an engine and a motor/generator (MG) used for drive, start and power generation. For example, when an accelerator opening is small in such a hybrid vehicle, a fuel supply to the engine is stopped, and the clutch is disengaged. By isolating the engine from a drive transmission part including the motor/generator, an EV drive is realized. With this operation, for example, when the hybrid vehicle coasts, there is no loss of electrical energy regeneration, due to engine friction, during a deceleration regenerative power generation by the motor/generator, and a regenerative amount is secured fully and efficiently. When the hybrid vehicle coasts down a long hill with an accelerator pedal released by a driver, the MG is used as the generator, and a frequency or the number of occurrences of recovering electricity by performing the regenerative power generation increases. In this situation, it is conceivable that a situation will often occur where a battery that stores the regenerative power or electricity becomes fully charged (that is, it is conceivable that a SOC (a capacity of charge of the battery) exceeds a specified value and the regeneration becomes impossible will often occur). Thus, where the SOC exceeds the specified value, in order to prevent an overcharge of the battery, regenerative braking by the MG is controlled or restrained (or suppressed). Where the regenerative braking is restrained even though the driver releases the accelerator pedal, hybrid systems are taught in, for example, Japanese Patent Provisional Publication Nos. 2004-162534 and 2006-306328 in which a clutch arranged between the engine and the motor is engaged, and the deceleration is ensured by the engine friction.